A falling stone accelerates at a constant rate of 10 m/s2
. It is
dropped from rest down a deep well, and 3 s later a splash is
heard as it hits the water below.
a) How fast will it be moving as it hits the water?
b) What will be its average speed over the three seconds?
c) How deep is the well?
d) What have you assumed about the speed of sound?
To answer these questions, we can use the kinematic equations of motion to analyze the stone's motion. Here's how we can approach each part:
a) How fast will it be moving as it hits the water?
To find the final velocity (v) of the stone when it hits the water, we can use the equation:
v = u + at
where:
- v is the final velocity,
- u is the initial velocity (which is 0 since the stone is dropped from rest),
- a is the acceleration (given as 10 m/s^2), and
- t is the time taken (given as 3 seconds).
Substituting the given values into the equation:
v = 0 + (10 m/s^2)(3 s)
v = 30 m/s.
Therefore, the stone will be moving at a velocity of 30 m/s when it hits the water.
b) What will be its average speed over the three seconds?
The average speed (v_avg) is calculated by dividing the total distance covered by the total time taken. In this case, since the stone is falling straight down the well, the distance traveled is equal to the depth of the well.
Since the well's depth is unknown, we'll denote it as "d" for now.
Using the equation for average speed:
v_avg = d / t
Substituting the given values:
v_avg = d / 3 s
We don't have enough information to find the exact average speed without knowing the depth of the well.
c) How deep is the well?
To find the depth of the well (d), we can use the equation of motion that relates distance, initial velocity, time, and acceleration:
d = u*t + (1/2)*a*t^2
Since the stone is dropped from rest (u = 0), the equation simplifies to:
d = (1/2)*a*t^2
Substituting the given values:
d = (1/2)*(10 m/s^2)*(3 s)^2
d = 45 m.
Therefore, the depth of the well is 45 meters.
d) What have you assumed about the speed of sound?
In this problem, we assumed that the speed of sound is constant and unaffected by any external factors. The splash is heard exactly 3 seconds after the stone is dropped, which indicates that the speed of sound is much faster than the speed of the stone.